Abstract: Contemporary Federated Learning (FL) is bottlenecked by the rigid distinction between static parameters and dynamic data, forcing a reliance on computationally expensive edge training and massive server-side aggregation bandwidth. This paper introduces Fluid Federated Learning (FFL), a paradigm that unifies parameter and data spaces to overcome these physical constraints. We propose three architectural contributions: (1) Federated State-Space Duality (F-SSD), which exploits the mathematical duality between Transformers and State-Space Models (SSMs) to treat recurrent states, rather than gradients, as the primary unit of federation, enabling privacy-preserving, interaction-driven learning; (2) The Neural Functional Server (NFS), which replaces linear averaging with a permutation-equivariant hypernetwork that aggregates heterogeneous client models by learning the geometry of the weight space; and (3) The Prism Protocol, a software-defined memory architecture that virtualizes the storage of massive foundation models. By leveraging the low intrinsic dimensionality of neural manifolds, the Prism Protocol utilizes Holographic Slicing, a technique grounded in the Johnson-Lindenstrauss lemma, to stream sparse, random projections of model weights directly from NVMe storage via io_uring. This allows commodity hardware to process "virtual batches" of terabyte-scale models, reducing memory requirements by orders of magnitude while preserving optimization fidelity. We demonstrate that FFL constitutes a computationally efficient, privacy-native substrate for the next generation of autonomous AI agents.